Introduction

Photosynthesis in global terrestrial ecosystems is a key driver of the land carbon sink, which removes 30% of CO2 from anthropogenic emissions of carbon1. The capacity of global photosynthesis to fix atmospheric CO2 depends on temperature, water and many other factors (e.g., nutrients and VPD)2,3. Under controlled conditions, leaf-scale photosynthesis first increases with warming until a maximum rate is reached defining an optimum temperature (Topt), after which it decreases with additional warming4,5,6. Topt is linked to the maximum gross primary productivity (GPP) of terrestrial ecosystems7 and represents an essential ecophysiological variable for modeling the global interactions between the terrestrial biosphere and the atmosphere8.

Differences in Topt across ecosystems, inferred from in situ flux observations, have been documented9 and many studies have reported that Topt is closely associated with the mean air temperature of a region8,10. For example, vegetation Topt is found to be higher in warmer areas as compared to cold regions6; a phenomenon suggesting long-term thermal adaptation. Whether Topt potentially can change over time as a consequence of the observed increase in temperature during the recent decades11 however remains unproven. Changes in the availability of water or nutrients12, CO2 levels10, and land cover13 may regulate the relationship between increasing temperatures and vegetation photosynthesis, which could cause temporal changes in Topt. These lines of evidence support the hypothesis that temporal changes in Topt of photosynthesis might potentially occur in a warming climate14. If Topt is increasing around the globe, it may support a continued increase of the global vegetation carbon sink15 rather than slowing down or reversing under the warming world16,17. Studying temporal changes in Topt at the global scale is therefore pivotal to better understand the response of the global carbon cycle to global warming18.

We define Topt as the monthly mean temperature at which GPP is highest within a given spatiotemporal “window” (5 years temporal window and 10 × 10 pixels of spatial window). Using multiple satellite-derived estimates for GPP and reanalysis climatic data sets, we first estimate the temporal dynamics of ecosystem Topt at the global scale during the period 1982 to 2016. We then study potential forcing variables of the changing Topt and attempt a coarse extrapolation of potential changes in Topt for 2017–2100 using the outputs of Coupled Model Intercomparison Project Phase 6 (CMIP6) under various climatic scenarios.

Results

Global increase in Topt

Changes in Topt are detected using a 5-year temporal moving window and a 1° spatial window (Supplementary Fig. 1) with multiple satellite-based products of GPP proxies (NIR GPP, KNDVI, NDVI, EVI) that are independent on climate variables as input (see Methods and Supplementary Table 1). The results indicate that the global average Topt based on NIR GPP has significantly (p < 0.05) increased from 18.64 ± 5.0 (mean ± std) to 19.18 ± 5.1 °C, with an average rate of 0.017 ± 0.002 °C y−1 (Fig. 1A) over the last 35 years. The increase in Topt was supported by increasing Topt derived from other temperature independent GPP proxies (KNDVI, NDVI and EVI). The majority of grid cells (69.6%) have a higher Topt in the period 2012-2016 than in the period 1982–1986 (Fig. 1B). A higher Topt in the later period (2010–2014) than in the earlier period (2001–2005) was also observed for most sites included in FLUXNET (Supplementary Fig. 2). Moreover, increases in Topt are found with different spatiotemporal windows (Supplementary Fig. 3), different combinations of GPP and temperature data sets (Supplementary Fig. 4), different temporal composition of GPP data sets (Supplementary Fig. 5), a larger body of different vegetation productivity proxy products (Supplementary Figs. 6, 7), different temperature data sets (Supplementary Fig. 8), and different methods used to smooth the response curve of vegetation productivity to temperature (Supplementary Fig. 9), demonstrating the robustness of the observed patterns.

Fig. 1: Global increase in Topt of ecosystem photosynthesis.
figure 1

A Temporal dynamics of Topt for four GPP data sets with a 5-y temporal window and a 1° spatial window for 1982–2016. The solid lines indicate the dynamics of Topt, and the shaded areas represent the 95% confidence interval of Topt. The dashed black line indicates the trend in Topt based on the NIR GPP data set. B Histogram of the difference in Topt between the first period (1982–1986) and the last period (2012–2016) for all 1° grids (n = 7971) derived from the NIR GPP data sets. The density function represents the standardized frequency (the sum of the area between x-axis and density function is 1). C Spatial patterns of trends in Topt derived from the NIR GPP data sets using a 5-y temporal window and a 1° spatial window for 1982–2016. The black points denote significant trends (p < 0.05). Dark gray indicates areas where Topt could not be successfully retrieved (see Methods, Supplementary Fig. 1d) for more than 40% of the temporal windows considered, and light gray indicates irrigated cropland and areas with sparse or no vegetation.

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The spatial patterns of the temporal trend of increasing Topt indicate that Topt significantly (p < 0.05) increased over 22.6% of the global terrestrial ecosystems (Fig. 1C), whereas a significantly (p < 0.05) negative trend in Topt is observed only for 6.0% of the global terrestrial ecosystems, mainly in western Siberia, savannas, and grasslands in northern Australia and southern Africa. The increase in Topt is closely associated with the increase in temperature from 1982 to 2016, both at the global scale and for different climatic zones (Supplementary Fig. 10). Globally, Topt is lower than the 80th percentile of temperature (Supplementary Fig. 10), indicating that Topt is generally lower than extreme warm air temperatures. The difference between Topt and the upper air temperature percentiles is particularly pronounced in tropical zone, where Topt is much lower than the 50% temperature percentiles. In contrast, Topt generally exceeds the 90th percentile of temperature in the polar zone (Supplementary Fig. 10), indicating that air temperature is markedly lower than Topt in this biome.

Drivers of increasing Topt

The complex co-regulation of various climatic factors to vegetation growth makes it challenging to derive contributions of these factors to vegetation change solely based on earth observation data. We thus used monthly GPP data sets simulated by process-based dynamic global vegetation models coupled by “Trends and drivers of the regional scale sources and sinks of carbon dioxide” (TRENDY, version 9) under four scenarios (S0, S1, S2, and S3, see Methods and Supplementary Table 2) to investigate the relative importance of drivers controlling changes in Topt. A good agreement between satellite and modelling derived Topt under the standard scenario (S3) reinforces confidence in the modelling simulations (Supplementary Fig. 11). We used the TRENDY modelling simulations to identify the forcing variables driving the increasing Topt, by comparing the differences between the trend in Topt from S3 and other simulations (see Methods and Supplementary Table 2). Globally, the simulation driven only by climate (CL) shows a Topt trend much closer to the standard scenario (S3, CO2 + CL + LC) than trends under scenarios that are driven only by either CO2 or LC (Fig. 2A), suggesting that climate change plays the most important role in controlling increasing Topt. The contribution of individual climate factors (e.g., temperature, precipitation, and radiation) cannot be differentiated due to the combined use of climate variables as input for the TRENDY models. However, the simulations from the LPJ-GUESS model allow to study the impact of individual climate forcing variables on Topt (Fig. 2B).

Fig. 2: Forcing variables of changes in Topt.
figure 2

A Trends in Topt from Earth observation data (EO) and from multi-model mean (TRENDY) of dynamic global vegetation models under different conditions: driven by varying CO2 only (CO2), driven by climate change only (CL), driven by land cover change only (LC), driven by varying CO2 and climate change (CO2 + CL), and driven by all above factors (CO2 + CL + LC) varying. The numbers superimposed on the bars denote the magnitude of trends in Topt under the different scenarios. B Trends in Topt from the LPJ-GUESS model under different conditions: driven by all factors varying (ALL), driven by varying temperature only (T), driven by varying CO2 only (CO2), driven by varying nitrogen deposition only (NDE), driven by varying precipitation only (PRE), and driven by varying solar radiation only (RAD). The numbers superimposed on the bars denote the magnitude of trends in Topt under the different scenarios. The error bars indicate 95% confidence interval of trends in Topt. C The relationship between the trend in satellite-observed Topt and the trend in a 5-y moving window of mean air temperature derived from the ERA5 data set for 1982–2016. D The consistency between the trend in satellite-observed Topt and the trend in the 5-y moving window of mean air temperature derived from the ERA5 data set. +-, increasing Topt and decreasing T; ++, increasing Topt and increasing T; --, decreasing Topt and decreasing T; -+, decreasing Topt and increasing T; n = 5323. Gray indicates irrigated cropland and areas with sparse or no vegetation.

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Similar to the simulations of TRENDY, we show a good agreement in Topt estimates based on satellite observations and the LPJ-GUESS model to support the validity of modelling simulations of Topt (Supplementary Fig. 12 and Supplementary Table 3). The simulation driven by varying temperature only (T) shows the highest increasing trend in Topt, which is more similar to the simulation under standard conditions, compared with trends in Topt under other simulations with a varying CO2 level only (CO2), varying nitrogen deposition only (NDE), varying precipitation only (PRE), and varying solar radiation only (RAD) (Fig. 2B). The modelling results obtained from these factorial simulations thereby suggest that air temperature is the most important climate factor for changes in Topt, followed by CO2 level and solar radiation. Furthermore, satellite observations also show that changes in temperature has the largest relative importance (71.12%) for the changes in Topt (Supplementary Fig. 13).

We also evaluate the relationship between satellite-observed Topt and its main climatic driver (air temperature). The trend in air temperature is binned into 100 groups, and the mean trend in Topt in each group is derived. The trend in satellite-observed Topt is significantly positively correlated (r = 0.66, p < 0.01) with the trend in mean air temperature in a 5-y moving window derived from the ERA5 data set (Fig. 2C). The trends in Topt and mean air temperature are consistent in most areas around the world, accounting for 65.1% of the area under analysis, with 64.5% of the area indicating consistently positive trends (++) and 0.06% indicating negative trends (--) (Fig. 2C). The trends in Topt and temperature (+- or -+) are found to be inconsistent in scattered regions in western Siberia, eastern China, and south-central Africa, totaling an area of 34.9%. As compared to the consistency found between Topt and temperature, the majority of pixels (57.5%) showed inconsistency (+- or -+) between trends in Topt and trends in precipitation (Supplementary Fig. 14) also supporting the key importance of temperature as a driver of the observed trends in Topt.

Projected changes in Topt

Projected changes in Topt and its relationship with increasing future air temperatures are estimated by deriving the multi-model mean historical and projected Topt from 23 CMIP6 models. We first compare the consistency between Topt derived from the historical CMIP6 models and from satellite observations (NIR GPP) using a 5-y temporal window and a 5° spatial window, which showed a good agreement (Supplementary Fig. 15). Similarly, the trends in Topt, the monthly mean temperature, and monthly maximum temperature derived from CMIP6 models are simulated (Fig. 3A) under scenarios of future climate (Supplementary Fig. 16). Topt under the SSP245 scenario increased at a rate of 0.027 ± 0.001 °C y−1, which is higher than the increases in monthly mean temperature (0.022 ± 0.001 °C y−1), but lower than the increases in monthly maximum temperature (0.035 ± 0.001 °C y−1) (Fig. 3A, Supplementary Fig. 16). This finding suggests that vegetation is adapting to future climatic warming but cannot match the rate of maximum warming. The projected increases in Topt are likely to slow down (Supplementary Figs. 16, 17), following the decrease in the level of emissions from SSP585 to SSP126, or even halt (SSP126) after 2050. A global increase in Topt in the last 5-y period (2096–2100) is evident under all scenarios, especially for SSP585, compared to the first 5-y period (2017-2021). Overall, under the SSP245 scenario, higher latitudes will have larger increase in Topt, matching a greater degree of warming in the future. Specifically, polar and cold areas are expected to have the largest increases in Topt (2.08 and 2.28 °C), together with the highest increase in monthly maximum temperature (2.89 and 2.97 °C)), but lowest monthly mean temperature (1.50 and 1.79 °C). Temperate and arid areas will have the smallest increase in Topt (1.85 and 1.89 °C), together with lower increase in monthly maximum temperature (2.46 and 2.46 °C) but quite large monthly mean temperature (1.94 and 1.98 °C). Tropical areas face moderate increases in Topt (2.0 °C) (Fig. 3B, C), together with moderate increase in monthly maximum temperature (2.48 °C) but largest monthly mean temperature (2.10 °C) (Supplementary Fig. 16).

Fig. 3: Projected changes in Topt of ecosystem productivity under the SSP245 scenario.
figure 3

A Projected temporal change of Topt, monthly maximum temperature, and monthly mean temperature for 2017–2100. Topt is estimated from 23 CMIP6 models with a 5-y temporal window and a 5° spatial window for 2017–2100. The maximum and mean temperatures are calculated using the same spatio-temporal windows as for Topt. The solid lines indicate the dynamics of Topt, maximum temperature, and mean temperature, and the shaded areas represent the 95% confidence interval of the maximum temperature, optimal temperature, and mean temperature. B The difference in mean Topt of two 5-y periods, 2017–2021 and 2096–2100, under the SSP245 scenario at the global scale and for different climatic zones. The error bars indicate 95% confidence interval of the difference in Topt. C Spatial patterns of the difference in Topt between two periods (2017–2021 and 2096–2100) under the SSP245 scenario. Gray indicates irrigated cropland and areas with sparse or no vegetation. Dark gray pixels indicate areas with Topt successfully extracted by less than 15 models.

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Discussion

Our study shows a global increase in Topt of ecosystem photosynthesis over the last four decades, which suggests an acclimation of terrestrial ecosystems to increasing temperatures under global warming. We further demonstrate that increasing temperatures are the key driver for the increasing Topt. This finding is partly supported by a local-scale study19. Spatial variations in the increase of Topt are also evident, showing a substantially lower Topt in colder areas compared to warmer areas6. Moreover, the increase in Topt is not uniform across space, with a higher increase in Topt in cold and arctic areas, which is likely related to the rapid warming in the northern high latitudes (arctic warming)20. An increase in temperature can affect Topt in different ways: Firstly, at the leaf level, changes in temperature can regulate photosynthetic Rubisco activity and electron transport, which is the principal mechanism controlling photosynthesis11. The capacity of electron transport and/or the thermal stability of Rubisco can therefore determine the acclimation of vegetation photosynthesis to increasing temperature21. However, our paper mainly focuses on the changes in Topt at ecosystem level based on satellite observations and model simulations (no long term thermal acclimation included in the models). We acknowledge that it cannot be inferred from this analysis whether the above mentioned thermal acclimation occurred at leaf level globally or not, although field observations already showed thermal acclimation at ground level in many different regions8,9,19. Secondly, higher temperatures induced higher vapor-pressure deficits (VPD, a proxy of atmospheric aridity)22 could lead to stomatal closure to reduce the loss of water at the cost of a decrease in CO2 exchange (productivity)23, which may increase vegetation resistance to increasing temperatures. However, at the ecosystem level, increasing temperatures may drive changes in vegetation composition or lead to species adapting to higher temperature tolerance, which could contribute to the Topt increases. This is particularly evident in the Northern hemisphere, woody encroaching into tundra biome due to climate warming24,25, which probably increase Topt.

Other factors (e.g. precipitation and CO2 level) also affect Topt (Fig. 2A) by altering the relationship between vegetation productivity and temperature. Firstly, the responses of Topt to climatic variables can be affected by water availability, especially in water-limited areas, where the extent to which precipitation and solar radiation exerts control on Topt, are largely dependent on dryness conditions12. This is likely attributed to the arid conditions that result in water scarcity within the soil, limiting vegetation’s ability to uptake water causing plants to close their stomata to mitigate water loss26, consequently reducing photosynthesis. Moreover, dryness can increase the risks of dehydration and heat stress, reducing photosynthesis27. Elevated CO2 could promote increase in Topt for plant growth by enhancing photosynthetic efficiency, improving water and nutrient use, and thereby enabling better thermal tolerance21,28,29. However, a few areas showed significantly decreasing Topt, such as southern Africa, western North America, and the northwestern Amazon rainforest. The decrease in southern Africa and western North America could be related to a regional cooling trend in these areas (Fig. 2D), while the decrease in the northwestern Amazon rainforest could be related low quality of the optical satellite dataset in this region due to cloud cover30.

A globally increasing Topt can have important implications for how terrestrial ecosystems are studied and for their functioning. Firstly, some studies have assumed that Topt is constant10, which is expected to be breached by the increasing temperatures in the foreseeable future31. The continuation of increasing temperatures would then be expected to have increasingly adverse impacts on ecosystems4. Our results, however, suggest thermal acclimation of ecosystems to increasing temperatures, which could to some extent delay the adverse effects as compared to what is currently expected31. Specifically, acclimation of global ecosystem photosynthesis to the increasing temperature implies that global warming will have less negative impacts on ecosystem productivity, which may eventually lead to a longer period of greening trend (carbon uptake) in the future than previously thought. For example, assuming a constant Topt, Zhang et al.31 reported a much earlier future point in time when summer temperatures would exceed Topt under future warming scenarios than the point in time when the temperature would negatively affect ecosystem GPP under all scenarios of future emissions, which could be partially attributed to neglecting thermal acclimation. Secondly, the acclimation of ecosystems to increasing temperatures could account for the decrease in the relative contribution of temperature to vegetation productivity32. Lastly, ecosystem acclimation also indicates the increase of heat tolerance of global ecosystems by adjusting their traits and physiological processes (e.g., modifying their phenology, growth patterns, and metabolic functions) in response to changing environmental conditions, which would allow ecosystems to better cope with extreme climate events.

A recent study however shows insignificant changes in ecosystem-scale Topt during recent decades6, which is different from our results. We have looked into this apparent discrepancy and have found that the difference may be attributed to the several reasons: Firstly, Huang, et al.6 used observations from a 10-year temporal window without including a spatial window10, which could lead to insufficient observations for the extraction of Topt (Supplementary Figs. 18, 19) thereby creating larger uncertainty in the Topt assessment ultimately concealing subtle trends. Secondly, the results reported by Huang, et al. 6 were based on the monthly mean of daily maximum temperatures (\({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{max }}}}\)), while we use the monthly mean of daily mean temperatures. Therefore, we examined the changes in Topt using both \({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{max }}}}\) and the monthly mean of daily mean temperatures (\({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{mean}}}}\)) and found that both of them produced globally increasing trends, and both trends are highly consistent (Supplementary Fig. 20). This suggests that different temperature metrics have little impact on the globally increasing trends in Topt. Thirdly, based on our method, we also use the same NDVI data set (used in Huang’s paper) to estimate Topt from 1982 to 2016 (Supplementary Fig. 6c). Trends in Topt derived from these data sets are generally consistent, which also suggests a globally increasing trends in Topt. Lastly, we use a fitting method of the Savitzky-Golay filter to fit 90% of GPP as a function of temperature, where Topt is extracted at a point of maximum GPP. This fitting approach makes the output less sensitive to noise in the original GPP, which is considered an advantage over the direct use of the maximum of 90% of GPP to calculate Topt applied in the previous study.

Our findings may be subject to some limitations. Firstly, good agreements of trends in Topt derived from different vegetation proxies were found across global regions, except for tropical rainforests (Supplementary Figs. 3–6). This may be caused by the relatively poor data quality of the original AVHRR satellite data due to cloud cover and signal saturation of NDVI in these tropical areas30. Secondly, to extract Topt, we used cubic convolution interpolation to resample the GPP data sets to 0.1° to match the spatial resolution of the climate data sets, which may introduce bias in areas characterized by high spatial variability. Thirdly, we used spatial windows to obtain sufficient observations to extract Topt. However, the window size could affect the extraction of Topt because plant function type within different size of windows may different, especially in the areas with high spatial variability. However, we found similar spatial patterns of Topt trend, using different sizes of spatial, suggesting the limited impacts of varying size of moving window on the Topt. Lastly, our study shows that global ecosystem Topt will continue to increase under global warming. However, these results are mainly derived from CMIP6 model simulations, which rely on the response equations of ecosystem photosynthesis to climate factors and human emissions. These results should be interpreted with caution, particularly under the climate scenario of SSP585, because thermal acclimation extending beyond 37 °C is uncertain11.

Our study document a widespread increase in Topt at the global scale, but we cannot yet provide a detailed answer to whether the changes in Topt over the last four decades are due to long-term genetic adaptation of the vegetation or to a short-term physiological response of the vegetation to climate change. More studies conducted at the species level9,19 are needed to resolve this question. Our study only involves changes in the optimal temperature of photosynthesis, and further research should also be targeted towards exploring the changes in Topt for ecosystem respiration and net ecosystem productivity and their inflection points under a projected warming world33. These studies will be critical for deepening our understanding of the exchange of carbon and energy in terrestrial ecosystems with implications for current efforts in achieving carbon neutrality.

Methods

GPP proxy data sets

Many studies have suggested that Near-infrared reflectance (NIR) has high correlations with GPP and it is at the same time less sensitive to non-vegetation objects in most ecosystems34. We therefore used a monthly GPP data set to estimate Topt, derived from satellite-based NIR, covering the period from 1982 to 2018 with a spatial resolution of 0.05°35. NIR GPP is generated independent on climate variables as input for the calculation of the product. Furthermore, to test the robustness of our results we also used four other data sets that are independent on temperature data sets to extract Topt. This involved the use data sets from vegetation indices including 3rd generation of Global Inventory Monitoring and Modeling System (GIMMS 3 g) normalized difference vegetation index (NDVI)36, 4th generation leaf area index (LAI) (GIMMS LAI4g)37, the MODIS NDVI, the MODIS enhanced vegetation index (EVI) and MODIS kernel NDVI (KNDVI)38 representing two different types of satellite sensor systems. The GIMMS NDVI data set represents the longest continuous time series of vegetation indices, covering from 1982 to 2016 with a 15-d temporal resolution and 1/12° spatial resolution. The GIMMS LAI4g share the same spatial and temporal resolution with GIMMS NDVI, but covers from 1982 to 2015. The monthly MODIS NDVI, and EVI data sets (MOD13C2) cover from 2001 to 2016 with 0.05° spatial resolution. Monthly MODIS KNDVI is produced from MOD13C2 red and NIR reflectance from 2001 to 201638. KNDVI is a nonlinear NDVI designed to have a higher sensitivity to vegetation biophysical and physiological processes, and thus is reported to have a more accurate estimation of terrestrial photosynthesis38.

In addition, five other data sets were used to test the robustness of the estimation of Topt, but were kept here secondary data sets, as these to some extent make use of temperature information in the modelling of GPP, that could potentially cause spurious co-varying trends with Topt: Improved (light use efficiency) LUE GPP39, Global Land Surface Satellite (GLASS) GPP40, solar-induced chlorophyll fluorescence (SIF) GPP (GOSIF GPP)41, spatial contiguous SIF (CSIF)42, FLUXCOM GPP43, and FLUXSAT GPP data sets. The Improved LUE GPP data set is based on the Monteith’s LUE approach. The equation applied is improved with optimized spatiotemporal LUEs, GIMMS3g of the canopy fraction of photosynthetically active radiation (FPAR), and meteorological information from Modern-Era Retrospective analysis for Research and Applications, Version 2, (MERRA-2)39. This global monthly GPP is produced at a 1/12° spatial resolution and covers 1982-2016. GLASS GPP is produced using a model of LUE, which is driven by four variables and was found to be able to accurately estimate the spatial and temporal dynamics of GPP40. This data set covers the period 1982–2018 and is provided with an 8-d temporal resolution and a 0.05° spatial resolution. We used.

SIF is considered a more direct indicator of plant photosynthesis (GPP)44. The GOSIF GPP data set was produced from SIF data from Orbiting Carbon Observatory-2 (OCO-2), data for terrestrial surface vegetation and temperature from Moderate Resolution Imaging Spectroradiometer (MODIS), and MERRA-2 meteorological reanalysis data41. These 8-d GPP data cover 2001 to 2020 with a 0.05° spatial resolution. FLUXNET GPP data consist of globally distributed eddy-covariance observations of fluxes of carbon and energy. Eddy covariance fluxes of FLUXNET and climate data were used to derive FLUXCOM GPP by upscaling methods (machine learning)43. Seasonal variations in the FLUXCOM data set were found to be consistent with atmospheric inversion-based carbon fluxes43. This monthly GPP data set covers 2001 to 2015 and is provided at a 1/12° spatial resolution. Daily FLUXSAT GPP data set provided at 0.05° spatial resolution was produced by training a neural network with FLUXNET 2015 eddy covariance tower sites data and MODIS reflectance data from 2000 to 202045,46.

All of the above GPP and vegetation index data sets were resampled to 0.1° using cubic convolution interpolation to match the spatial resolution of the temperature data set. The maximum-value composite (MVC) method47 was applied to produce all GPP and vegetation index data sets as monthly observations to match the temporal resolution of the temperature data set.

FLUXNET 2015 observations

We used flux-tower (FLUXNET2015) based GPP and air temperature to calculate the optimal temperature. The FLUXNET2015 dataset provides measurements of CO2, water, and energy exchange between the biosphere and the atmosphere, and other meteorological measurements (e.g., air temperature), from 212 sites around the globe, covering the periods before 201548. The sites having more than 10 years of daily observations of GPP and temperature during 2001–2014 were chosen for the analysis (34 sites, Supplementary Table 2). We estimated the optimal temperature for two different 5-year periods: 2001–2005 and 2010–2014 (It should be noted that the observations at some sites might not be available in 2001–2002 or 2013–2014, and observations in 2003–2007 or 2008–2012 were used as alternatives). We also excluded the sites with a failure to capture the optima temperature.

Climatic data

To estimate the robustness of the extraction of Topt, we used two data sets of monthly mean temperature (Tmean) to derive the optimal temperature (\({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{mean}}}}\)) based on mean temperatures: CRU TS (Climatic Research Unit gridded Time Series) and ERA5. The ERA5 data set of monthly Tmean with a 0.1° spatial resolution was produced by the Copernicus Climate Change Service at the European Centre for Medium-Range Weather Forecasts (ECMWF). The data set is the fifth generation reanalysis of data for the global climate (ERA5-land)49. The CRU monthly Tmean is derived from an extensive network of observations from meteorological stations gridded at 0.5° spatial resolution from the period 1901–202050. We used \({{{\rm{T}}}}_{{opt}}^{{mean}}\) as basis for the optimal temperature (Topt). Daily maximum temperature, however, is also important for the thermal acclimation of vegetation. We therefore also used the monthly means in the ERA5 data set of daily maximum temperatures (Tmax) to derive the optimal temperature (\({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{max }}}}\)) and compared it with \({{{\bf{T}}}}_{{{\boldsymbol{opt}}}}^{{{\boldsymbol{mean}}}}\) (Supplementary Fig. 20). The monthly mean ERA5 Tmax was derived from hourly ERA5 temperatures with a 0.1° spatial resolution. We averaged Tmax to into a monthly data set to match the spatiotemporal resolution of the ERA5 monthly mean temperature.

CMIP6 data sets

We used data for GPP and temperature from 23 Earth system models (ESMs) (Supplementary Table 4) in Phase 6 of the Coupled Model Intercomparison Project (CMIP6) to produce the projected Topt. The scenarios used in CMIP6 combine Shared Socioeconomic Pathways (SSPs) and targeted radiative forcing levels for the end of the 21st century51. SSP126, SSP245, SSP370, and SSP585 represent various emissions of CO2 from the lowest to the highest level51. We used data sets of monthly GPP and temperature for 2017 to 2100 under different scenarios (SSP126, SSP245, SSP370, and SSP585) to derive the projected changes in Topt.

Other auxiliary data sets

Global climatic zones

The current map of climatic zones is an improved map of the Köppen-Geiger classification of climate with a 1/12° spatial resolution (Supplementary Fig. 21). Multiple independent data sources have been used to maximize the accuracy of the classification of climatic zones52.

ESA CCI land cover

We used the ESA climate change initiative (CCI) land-cover map for 200053 with a spatial resolution of 300 m to derive masks of irrigated cropland and areas with sparse or no vegetation. The masked areas were: irrigated cropland, barren land, permanent snow, and ice-covered areas (Supplementary Fig. 21).

These auxiliary data sets were resampled to 1° using nearest-neighbour interpolation to match the spatial resolution of the Topt data.

Analysis

Extraction of Topt

We followed the basic concept of a previously suggested method6,9 to derive Topt. Unlike previous studies, however, we extracted Topt by testing the relationships (response curves) between monthly GPP and monthly mean temperature (both with 1° spatial resolution) within a 5-y temporal window (12 × 5) and a 1° spatial window (10×10) (different spatio-temporal windows were also tested) (Supplementary Fig. 3) to secure enough observations for a statistically robust extraction of Topt. GPP and its corresponding T within a spatiotemporal window were grouped into multiple bins by intervals of 0.5 °C. We used the 90% quantiles of GPP and T as the response of GPP to T for each bin, because other factors (e.g. residual cloud cover, sun-sensor viewing angle configuration and extreme climatic events) may also affect GPP. The Savitzky-Golay filter54 was then used to smooth the response curve to reduce data noise. Topt for the five years was defined as the T at which the corresponding GPP was at its maximum along the smoothed response curve (Supplementary Fig. 1). Areas from where Topt was extracted at the end of the curve were considered as areas of unsuccessful extractions, as a maximum could not be established (Supplementary Fig. 1d). For areas where Topt was successfully extracted, < 60% of all years were excluded. Masks were applied to exclude irrigated cropland and areas with sparse or no vegetation (Supplementary Fig. 21b).

Model simulations

TRENDY

To study the drivers of the changing Topt, we used six vegetation models (ISAM, LPJ-GUESS, LPX-Bern, ORCHIDEE, ORCHIDEEv3, and VISIT) for simulating monthly GPP at 0.5° spatial resolution during 1982 to 2016 under different conditions (Supplementary Table 3). GPP datasets from these models are based on photosynthetic light-response curves with different factors, including light level, leaf-internal CO2 concentration (so adjusted for stomatal response), water, nitrogen, phosphorus and temperature55,56. It should be noted that the short-term responses of vegetation to environmental factors have already been included in the land models, but long-term responses (i.e., thermal acclimation at leaf level) is not included. However, changes in the plant function type (PFT) have already been included in these models, which may lead to different Topt because the temperature ranges for optimal photosynthesis differ per PFT composition57,58. These models were driven by historical changes in three factors (atmospheric CO2, climate, and land cover)13. Specifically, under Scenario 0 (S0), all of the above factors are set as constant values (using the monthly recycling mean and variability of factors from 1901 to 1920 in the following periods: 1921–1940, 1941-1960, 1961-1980, 1981-2000, and 2000-2020). Scenario 1 (S1) was driven by varying atmospheric CO2, but constant climate and land cover. Scenario 2 (S2) was driven by varying atmospheric CO2 and climate, but constant land cover. Scenario 3 (S3) was driven by varying atmospheric CO2, climate, and land cover. We extracted Topt using a 5-y temporal window and a spatial window of 5×5 grid cells under all scenarios. The difference of changes in Topt between S1 and S0 (S1-S0) was then used to estimate the impact of CO2 on Topt. Similarly, S2-S1 and S3-S2 indicate the impact of climate change and land cover change, respectively (Fig. 2A). We used a different spatial window size (5×5) than for the extraction of Topt from satellite data sets, because of the relatively coarse spatial resolution of the forcing data used as input for the model. The importance of the size of the spatial window was tested and was found to have only a minor impact on the extraction of Topt (Supplementary Fig. 3).

LPJ-GUESS

Climate variables including temperature, precipitation, and solar radiation were combined into one variable in the TRENDY models, which impedes a quantification of the contribution of individual climate variables. We thus applied the Lund-Potsdam-Jena General Ecosystem Simulator (LPJ-GUESS) model59, forced by individual climate variables (temperature, precipitation, solar radiation, nitrogen deposition, and CO2), for simulating monthly GPP at 0.5° spatial resolution for the period 1982 to 2016. Global monthly atmospheric CO2 levels and historical monthly CRU climatic data sets (temperature, precipitation, radiation) at 0.5° spatial resolution from 1901 to 2020 were used to drive the model. In addition to the variables used to force the TRENDY models, we also included nitrogen deposition as a variable, which is an important factor for ecosystem photosynthesis. Firstly, model runs were forced with all factors varying (temperature, precipitation, solar radiation, CO2 level, and nitrogen deposition) under standard conditions (ALL) to simulate monthly GPP. Secondly, similar to the TRENDY simulations, the LPJ-GUESS model was forced with one varying factor while the remaining factors were kept constant (monthly recycling mean and variability from 1901 to 1920). Thirdly, the model-simulated GPP data sets were used to extract Topt with a 5-year temporal window and a spatial window of 5×5 grid cells under different conditions to evaluate the contribution of each forcing variables to the changing Topt (Fig. 2B).

Trend analysis

The Theil-Sen estimator and a Mann-Kendall trend test were used at the pixel level to assess historical (1982–2016) and projected (2017–2100) trends in Topt. Yue-Pilon prewhitening method was used to remove serial autocorrelations60 in time series of Topt which was calculated with a moving window. The significance level of p < 0.05 was applied to retain clear and coherent spatial clusters/patterns of trends. The Mann-Kendall trend test is a non-parametric test, which is robust against outliers and does not require the data to be normally distributed.

Relative importance analysis

We used a relative weight analysis approach61 to estimate to what extent the trend in Topt can be explained by the climatic factors. The relative importance is assessed using the “lmg” approach in a multiple regression62, where the trend in Topt is set as response variable and trends in temperature, precipitation and radiation as explanatory variables.